evaluates to 1 for all integers and for all positive real numbers. For negative non-integers where abs(n) is between consecutive whole numbers a and a+1 the function evaluates to a/(a+1) which also goes to 1.

(ii) 2151331

The negative part is just the sum of the numbers 1 to 2012 and the positive part is just the sum of the numbers 0 to 502.